Stream Order as a Measure of Sample Source Uncertainty

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Abstract
The Horton stream order at the outlet of a drainage basin is a direct measure of the uncertainty (entropy) of the source supplying any discrete particle or atom detected at the outlet. Ifmis the order of the main stream in a basin, the uncertainty that the source lies in the drainage area of anith order tributary is given bym‐i. This may be interpreted as representing the minimum number of tests or samples needed to find a single contamination source in a sequential search of a drainage basin. Similarly Scheidegger's consistent stream order may be interpreted as being the number of samples required to search a basin for a single source when the link magnitude of the outlet is known. Because natural streams usually have multiple contaminant sources and cannot be expressed as a simple branching process, a convenient estimate of the average number of samples needed to find a single source is given by (rb‐ 1) (m‐i) whererbis the bifurcation ratio.